Physics

15)A small ball of mass m is aligned above a larger ball of mass M = 1.2 kg (with a slight separation, as with the baseball and basketball of Figure (a)), and the two are dropped simultaneously from height h = 2.4 m. (Assume the radius of each ball is negligible compared to h.) (a) If the larger ball rebounds elastically from the floor and then the small ball rebounds elastically from the larger ball, what value of m results in the larger ball stopping when it collides with the small ball? (b) What height does the small ball then reach (see Figure (b))?

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  1. Assume on rebound they have the following velocities:
    large ball: V, in upward direction
    small ball: V, in downward direction

    you can calculate V from the height of the drop.
    Assume conservation of momentum, and if needed, conservation of energy.

    Momentum
    MV-mV=M*0+mV'
    V'=(M/m -1) V
    Conservation of energy
    MV^2 + mV^2=mV'^2
    MV^2+ mV^2=m(M/m-1)^2*V^2
    notice V^2 divides out.
    a bit of algebra to solve for m ensues, but it is tolerable.

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